Position Error Bound for UWB Localization in Dense Cluttered Environments DAMIEN B. JOURDAN, Member, IEEE Athena Technologies, Inc. DAVIDE DARDARI, Member, IEEE University of Bologna at Cesena Italy MOE Z. WIN, Fellow, IEEE Massachusetts Institute of Technology For most outdoor applications, systems such as Global Positioning System (GPS) provide users with accurate location estimates. However, similar range-only localization techniques in dense cluttered environments typically lack accuracy and reliability due, notably, to dense multipath, line-of-sight (LOS) blockage and excess propagation delays through materials. In particular, range measurements between a receiver and a transmitter are often positively biased. Furthermore, the quality of the range measurement degrades with distance, and the geometric configuration of the beacons also affects the localization accuracy. In this paper we derive a fundamental limit of localization accuracy for an ultrawide bandwidth (UWB) system operating in such environments, which we call the position error bound (PEB). The impact of different ranging estimation errors due to beacons distance and biases on the best positioning accuracy is investigated. The statistical characterization of biases coming from measurement campaigns can easily be incorporated into this analysis. We show that the relative importance of information coming from different beacons varies depending on the propagation conditions, such as whether the beacon is LOS or non-line-of-sight (NLOS). We show, in particular, that any a priori information knowledge on NLOS beacons can significantly improve the localization accuracy, especially in dense cluttered environments. Finally we put forth the concept of localization outage probability and ²-localization accuracy outage, and use them to characterize the quality of localization throughout the area. Manuscript received March 3, 2006; revised September 1, 2006; released for publication April 12, 2007. IEEE Log No. T-AES/44/2/926546. Refereeing of this contribution was handled by T. F. Roome. This research was supported, in part, by the Ministero dell’Istruzione, Universit` ae della Ricerca Scientifica (MIUR) under the Virtual Immersive Communications (VICom) project, the Institute of Advanced Study Natural Science & Technology Fellowship, the Charles Stark Draper Laboratory Robust Distributed Sensor Networks Program, the Office of Naval Research Young Investigator Award N00014-03-1-0489, and the National Science Foundation under Grant ANI-0335256. Part of the results of this research were presented at the IEEE International Conference on Communications, Istanbul, Turkey, June 2006. Authors' current addresses: D. B. Jourdan, Athena Technologies, Inc., 6876 Watson Court Warrenton, VA 20187, Email: (jourdan@alum.mit.edu); D. Dardari, WiLAB-DEIS, University of Bologna at Cesena, via Venezia 52, Cesena (FC), Italy, E-mail: (ddardari@ieee.org); M. Z. Win, Laboratory for Information and Decision Systems, Massachusetts Institute of Technology, 77 Massachusetts Ave, Cambridge, MA, E-mail: (moewin@mit.edu). 0018-9251/08/$25.00 c ° 2008 IEEE I. INTRODUCTION Since the Global Positioning System (GPS) became widely accessible [1], localization in the absolute frame (or geolocation) has found application in many different fields. In areas where there is a good line-of-sight (LOS) to GPS satellites, this technique provides a good estimate (within a few meters) of the user’s location on the Earth. However, in indoor and dense urban environments, geolocation has always been a more challenging problem for several reasons. The GPS signal is, for example, not strong enough to penetrate through most materials. As soon as an object hides the GPS satellite from the user’s view, the signal is corrupted. This constrains the usefulness of GPS to open environments, and limits its performance in forests or in dense urban environments, as retaining a lock on the GPS signals becomes more difficult. GPS typically becomes completely useless inside buildings. However there is an increasing need for accurate geolocation in cluttered environments, in addition to open spaces. In commercial applications for example, the tracking of inventory in warehouses or cargo ships is an emerging need. In military applications the problem of “blue force tracking,” i.e., knowing where friendly forces are, is of vital importance, especially in urban scenarios. To address the problem of geolocation in cluttered environments, we consider a network of fixed beacons (or anchor nodes) emitting ultrawide bandwidth (UWB) signals for ranging purposes. UWB technology potentially provides high ranging accuracy in cluttered environments [2—7] owing to its inherent delay resolution and ability to penetrate obstacles [8—13]. Further information on the fundamentals of UWB can be found in [14]—[18] and the references therein. We assume that the location of these beacons is known, for example because they are placed outside and can rely on GPS. The agent (or unknown node) estimates the ranges to these beacons to determine its position. These ranges are often obtained by estimating the time-of-arrival of the signal, for which several techniques exist [2, 3, 6, 19, 20]. The accuracy of range-only localization systems depends mainly on two factors. The first is the geometric configuration of the system, i.e., how the beacons are placed relative to the agent. The second is the quality of the range measurements themselves. If the range estimates to the beacons were perfect, then three beacons, placed at any (but distinct) locations would be sufficient to determine the agent position unambiguously in 2D, using any triangulation technique. In practice, however, these measurements are corrupted due to the propagation properties of the environment. Partial and complete LOS blockage (see Section II) lead, for example, to biased range estimates. Furthermore, the measurement variance IEEE TRANSACTIONS ON AEROSPACE AND ELECTRONIC SYSTEMS VOL. 44, NO. 2 APRIL 2008 613